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Continuity of the maximal operator in Sobolev spaces

Author: Hannes Luiro
Journal: Proc. Amer. Math. Soc. 135 (2007), 243-251
MSC (2000): Primary 42B25, 46E35, 47H99
Published electronically: June 30, 2006
MathSciNet review: 2280193
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Abstract: We establish the continuity of the Hardy-Littlewood maximal operator on Sobolev spaces $ W^{1,p}(\mathbb{R}^n)\,$, $ 1<p<\infty\,$. As an auxiliary tool we prove an explicit formula for the derivative of the maximal function.

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Additional Information

Hannes Luiro
Affiliation: Department of Mathematics and Statistics, University of Jyväskylä, P.O. Box 35 (MaD), 40014 University of Jyväskylä, Finland

Keywords: Maximal function, Sobolev spaces, continuity, regularity
Received by editor(s): June 4, 2004
Received by editor(s) in revised form: August 8, 2005
Published electronically: June 30, 2006
Additional Notes: The author was supported by the Academy of Finland, project 201015
Communicated by: Juha M. Heinonen
Article copyright: © Copyright 2006 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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